Korea's post offices are operated by the national government. There are more than 3,700 spread about the country, so you can find one easily no matter where you go. And yet, there's one just across my apartment building. Post offices have good services. They deliver so fast and it's very reliable. It delivers faster than what you think. When my mother in law sends some kimchi or other products to my sister in law, she goes to the post office in the morning. She said they deliver some goods in the morning so if she goes there in the morning, the goods that she wants to send will reach the destination earlier because they can bring her package on that same day.
There are different types of services if you want to send letters or package within Korea. You can send by "registered mail" (deunggi) where you can trace the route of delivery and it is given directly recipient. There's also the "next day service" (igilteukgeup), a service when you want to have something delivered the next day in most places throughout Korea. And the "door to door" (taekbae) service where you can call the post office and have the item picked up from your home or company. It is a good idea to use "Express Mail Office" (EMS) when sending a letter or package from Korea to another country which is quick and reliable. You can also use EMS to send kimchi, tea, marine products, and other products offered by the postal office.
In recent years, Koreas post offices have begun offering financial and other services like opening an account, get insurance and pay taxes and fees. Post Offices in Korea have good service but beware of the voice phishing where they use the named post office and telling you to pay something that you don't know.
Post offices are open from Monday-Friday but in large areas or cities, they are also open on Saturdays.